Method and apparatus for image reconstruction using a knowledge set

ABSTRACT

A method of constructing a non-uniform attenuation map ( 460 ) of a subject for use in image reconstruction of SPECT data is provided. It includes collecting a population of a priori transmission images and storing them in an a priori image memory ( 400 ). The transmission images not of the subject. Next, a cross-correlation matrix ( 410 ) is generated from the population of transmission images. The eigenvectors ( 420 ) of the cross-correlation matrix ( 410 ) are calculated. A set of orthonormal basis vectors ( 430 ) is generated from the eigenvectors ( 420 ). A linear combination of the basis vectors ( 420 ) is constructed ( 440 ), and coefficients for the basis vectors are determined ( 450 ) such that the linear combination thereof defines the non-uniform attenuation map ( 460 ).

This application claims the benefit of U.S. Provisional Application No.60/065,582 filed Nov. 12, 1997.

BACKGROUND OF THE INVENTION

The present invention relates to the art of diagnostic nuclear imaging.It finds particular application in conjunction with gamma cameras andsingle photon emission computed tomography (SPECT), and will bedescribed with particular reference thereto. However, it is to beappreciated that the present invention is also amenable to other likeapplications.

Diagnostic nuclear imaging, is used to study a radionuclide distributionin a subject. Typically, in SPECT, one or more radiopharmaceuticals orradioisotopes are injected into a subject. The radiopharmaceuticals arecommonly injected into the subject's blood stream for imaging thecirculatory system or for imaging specific organs which absorb theinjected radiopharmaceuticals. One or more gamma or scintillation cameradetector heads, typically including a collimator, are placed adjacent toa surface of the subject to monitor and record emitted radiation. Thecamera heads typically include a scintillation crystal which produces aflash or scintillation of light each time it is struck by radiationemanating from the radioactive dye in the subject. An array ofphotomultiplier tubes and associated circuitry produce an output signalwhich is indicative of the (x, y) position of each scintillation on thecrystal. Often, the heads are rotated or indexed around the subject tomonitor the emitted radiation from a plurality of directions to obtain aplurality of different views. The monitored radiation data from theplurality of views is reconstructed into a three dimensional (3D) imagerepresentation of the radiopharmaceutical distribution within thesubject.

One of the problems with this imaging technique is that photonabsorption and scatter by portions of the subject between the emittingradionuclide and the camera head distort the resultant image. Onesolution for compensating for photon attenuation is to assume uniformphoton attenuation throughout the subject. That is, the subject isassumed to be completely homogenous in terms of radiation attenuationwith no distinction made for bone, soft tissue lung, etc. This enablesattenuation estimates to be made based on the surface contour of thesubject. Of course, human subjects do not cause uniform radiationattenuation, especially in the chest.

In order to obtain more accurate radiation attenuation measurements, adirect measurement is made using transmission computed tomographytechniques. In this technique, radiation is projected from a radiationsource through the subject. The transmission radiation is received bydetectors at the opposite side. The source and detectors are rotated tocollect transmission data concurrently with the emission data through amultiplicity of angles. This transmission data is reconstructed into animage representation or non-uniform attenuation map using conventionaltomography algorithms. The radiation attenuation properties of thesubject from the transmission computed tomography image are used tocorrect for radiation attenuation in the emission data. See, forexample, U.S. Pat. Nos. 5,210,421 and 5,559,335, commonly assigned andincorporated herein by reference.

However, transmission computed tomography techniques suffer from theirown drawbacks. One such drawback is an undesirable increase in thepatient's exposure to radiation due to the transmission scan. Moreover,the transmission scan increase the costs associated with producingclinical SPECT images.

Additionally, the truncation of transmission data or transmissionprojections due to a relatively small detector size is a well knownproblem in SPECT. This problem is further exacerbated duringtransmission imaging of the chest by a three-detector SPECT system withfan-beam collimators. See, for example, G. T. Gullberg, et al., “Reviewof Convergent Beam Tomography in Single Photon Emission ComputedTomography,” Phys. Med. Biol., Vol. 37, No. 3, pp. 507-534, 1992. Thetruncation problem results in solving a rank deficient system of linearequations, which leads to reconstruction artifacts when commonreconstruction algorithms are applied. See, for example: J. C. Gore, etal., “The Reconstruction of Objects from Incomplete Projections,” Med.Phys., Vol. 25, No. 1, pp. 129-136, 1980; G. L. Zeng, et al., “A Studyof Reconstruction Artifacts in Cone Beam Tomography Using FilteredBackprojection and Iterative EM Algorithms,” IEEE Trans. Nucl. Sci.,Vol. 37, No. 2, pp. 759-767, 1990; S. H. Manglos, “Truncation ArtifactSuppression in Cone-Beam Radionuclide Transmission CT Using MaximumLikelihood Techniques: Evaluation with Human Subjects,” Phys. Med.Biol., Vol. 37, No. 3, pp. 549-5562, 1992; G. L. Zeng, et al., “NewApproaches to Reconstructing Truncated Projections in Cardiac Fan Beamand Cone Beam Tomography,” J. Nucl. Med., Vol. 31, No. 5, p. 867, 1990(abstract); and, B. M. W. Tsui, et al., “Cardiac SPECT Reconstructionswith Truncated Projections in Different SPECT System Designs,” J. Nucl.Med., Vol. 33, No. 5, p. 831, 1992 (abstract).

The present invention contemplates a new and improved technique forSPECT imaging which overcomes the above-referenced problems and others.

SUMMARY OF THE INVENTION

In accordance with one aspect of the present invention, a method ofconstructing a non-uniform attenuation map of a subject for use in imagereconstruction of SPECT data is provided. It includes collecting apopulation of a priori transmission images. The transmission images arenot of the subject. A cross-correlation matrix is generated from thepopulation of transmission images. Next, the eigenvectors of thecross-correlation matrix are calculated. A set of orthonormal basisvectors is generated from the eigenvectors. Finally, a linearcombination of the basis vectors is constructed, and coefficients forthe basis vectors are determined such that the linear combinationthereof defines the non-uniform attenuation map.

In accordance with a more limited aspect of the present invention, aKarhunen-Loève transform is employed to calculate the eigenvectors ofthe cross-correlation matrix.

In accordance with a more limited aspect of the present invention, theset of orthonormal basis vectors is constructed from a predeterminednumber of selected eigenvectors chosen from the eigenvectors of thecross-correlation matrix. The selected eigenvectors have correspondingeigenvalues larger than eigenvalues of non-selected eigenvectors.

In accordance with a more limited aspect of the present invention, thestep of determining coefficients for the basis vectors includesiteratively comparing projections of the set of orthonormal basisvectors having estimated coefficients with truncated transmissionprojections from the subject. Using a least-squares fit, coefficientsare selected which best match the projections of the set of orthonormalbasis vectors to the truncated transmission projections from thesubject.

In accordance with a more limited aspect of the present invention, thestep of determining coefficients for the basis vectors includesiteratively employing Natterer's data consistency conditions to relateemission data from the subject to transmission projections. Thetransmission projections are generated from projections of the set oforthonormal basis vectors having estimated coefficients. Using aleast-squares fit, coefficients are selected which generate thetransmission projections that best fulfill Natterer's data consistencyconditions.

In accordance with a more limited aspect of the present invention, notransmission scan of the subject is performed.

In accordance with a more limited aspect of the present invention, thepredetermined number of selected eigenvectors is less than or equal toapproximately 15% of all the eigenvectors.

In accordance with another aspect of the present invention, an imageprocessor for reconstructing images of a distribution of radioactivematerial in a patient being examined with a gamma camera is provided. Itincludes an emission memory which stores emission data collected by thegamma camera. An attenuation factor memory stores attenuation factorscalculated from a non-uniform attenuation map. A data processor takesthe emission data and corrects it for attenuation in accordance with theattenuation factors stored in the attenuation factor memory. Areconstruction processor takes corrected emission data from the dataprocessor and therefrom reconstructs an image representation of thedistribution of radioactive material in the patient. An a priori imagememory stores a priori transmission data from a plurality of a prioritransmission scans of a region of interest that is the same as thatbeing reconstructed. The transmission scans originate from subjectsother than the patient. A cross-correlation data processor constructs across-correlation matrix from the a priori transmission scans, and aneigenvector data processor calculates eigenvectors of thecross-correlation matrix. A basis data processor constructs a set oforthonormal basis vectors from the eigenvectors of the cross-correlationmatrix, and an iterative data processor computes coefficients for thebasis vectors such that a linear combination thereof defines thenon-uniform attenuation map.

One advantage of the present invention is that accurate non-uniformattenuation maps are achieved.

Another advantage of the present invention is the patients' radiationdosage is lessened by the elimination of transmission scans.

Yet another advantage of the present invention is that accuratenon-uniform attenuation maps are achieved from truncated transmissionscans.

Still further advantages and benefits of the present invention willbecome apparent to those of ordinary skill in the art upon reading andunderstanding the following detailed description of the preferredembodiments.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention may take form in various components and arrangements ofcomponents, and in various steps and arrangements of steps. The drawingsare only for purposes of illustrating preferred embodiments and are notto be construed as limiting the invention.

FIG. 1 is a diagrammatic illustration of a nuclear medicine gamma camerain accordance with aspects of the present invention; and,

FIG. 2 is a diagrammatic illustration showing a technique for theconstruction of a non-uniform attenuation map in accordance with aspectsof the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

With reference to FIG. 1, a diagnostic nuclear imaging apparatus orgamma camera 10 includes a subject support 12, such as a table or couch,which supports a subject being examined and/or imaged such as a phantomor patient. The subject is injected with one or moreradiopharmaceuticals or radioisotopes such that emission radiation isemitted therefrom. Optionally, the subject support 12 is selectivelyheight adjustable so as to center the subject at a desired height. Afirst gantry 14 holds a rotating gantry 16 rotatably mounted thereto.The rotating gantry 16 defines a subject-receiving aperture 18. In apreferred embodiment, the first gantry 14 is advanced toward and/orretracted from the subject support 12 so as to selectively positionregions of interest of the subject within the subject-receiving aperture18. Alternately, the subject support 12 is advanced and/or retracted toachieve the desired positioning of the subject within the subject-receiving aperture 18.

One or more detector heads 20 are adjustably mounted to the rotatinggantry 16 with varying degrees of freedom of movement. Optionally, thedetector heads 20 are circumferentially adjustable to vary their spacingon the rotating gantry 16. Separate translation devices 22, such asmotors and drive assemblies (not shown), independently translate thedetector heads 20 laterally in directions tangential to thesubject-receiving aperture 18 along linear tracks or other appropriateguides. Additionally, the detector heads 20 are also independentlymovable in radial directions with respect to the subject-receivingaperture 18. Optionally, the detector heads 20 selectively cant or tiltwith respect to radial lines from the center of the subject-receivingaperture 18. Alternately, a single motor and drive assembly controlsmovement of all the detector heads 20 individually and/or as a unit.

Being mounted to the rotating gantry 16, the detector heads 20 rotateabout the subject-receiving aperture 18 (and the subject when locatedtherein) along with the rotation of the rotating gantry 16. Inoperation, the detector heads 20 are rotated or indexed around thesubject to monitor radiation from a plurality of directions to obtain aplurality of different angular views.

Each of the detector heads 20 has a radiation-receiving face facing thesubject-receiving aperture 18 that includes a scintillation crystal,such as a large doped sodium iodide crystal, that emits a flash of lightor photons in response to incident radiation. An array ofphotomultiplier tubes receives the light and converts it into electricalsignals. A resolver circuit resolves the x, y-coordinates of each flashof light and the energy of the incident radiation. That is to say,radiation strikes the scintillation crystal causing the scintillationcrystal to scintillate, i.e., emit light photons in response to theradiation. The photons are directed toward the photomultiplier tubes.Relative outputs of the photomultiplier tubes are processed andcorrected to generate an output signal indicative of (1) a positioncoordinate on the detector head at which each radiation event isreceived, and (2) an energy of each event. The energy is used todifferentiate between various types of radiation such as multipleemission radiation sources, stray and secondary emission radiation,transmission radiation, and to eliminate noise. An image representationis defined by the radiation data received at each coordinate. Theradiation data is then reconstructed into an image representation of theregion of interest.

Optionally, the detector heads 20 include mechanical collimators 24removably mounted on the radiation receiving faces of the detector heads20. The collimators 24 preferably include an array or grid of lead orotherwise radiation-absorbent vanes which restrict the detector heads 20from receiving radiation not traveling along selected rays in accordancewith the data type being collected (i.e., parallel beam, fan beam,and/or cone beam).

One or more radiation sources 30 are mounted across thesubject-receiving aperture 18 from the detector heads 20. Optionally,they are mounted between the detector heads 20 or to the radiationreceiving faces of opposing detector heads 20 such that transmissionradiation from the radiation sources 30 is directed toward and receivedby corresponding detector heads 20 on an opposite side of thesubject-receiving aperture 18. In a preferred embodiment, thecollimators 24 employed on the detector heads 20, in effect, collimatethe transmission radiation. That is to say, the collimators 24 restrictthe detector heads 20 from receiving those portions of transmissionradiation not traveling along rays normal (for parallel beamconfigurations) to the radiation receiving faces of the detector heads20. Alternately, other collimation geometries are employed and/or thecollimation may take place at the source.

In a preferred embodiment, the radiation sources 30 are line sourceseach extending the axial length of the respective detector heads 20 towhich they correspond. Preferably, the lines sources are thin steeltubes filled with radionuclides and sealed at their ends. Alternately,the radiation sources 30 are bar sources, point sources, flatrectangular sources, disk sources, flood sources, a tube or vesselfilled with radionuclides, or active radiation generators such as x-raytubes. Alternately, one or more point sources of transmission radiationmay be utilized.

With reference again to FIG. 1, the running of an imaging operationincludes a reconstruction technique wherein emission data isreconstructed via an image processor 100 into an image representation ofthe distribution of radioactive material in the patient. Of course, thereconstruction technique changes according to the types of radiationcollected and the types of collimators used (i.e. fan, cone, parallelbeam, and/or other modes). In any case, emission radiation from thepatient is received by the detector heads 20, and emission projectiondata is generated. The emission data normally contains inaccuraciescaused by varying absorption characteristics of the patient's anatomy.Optionally, a transmission scan is also performed such that transmissionradiation from one or more of the transmission radiation source 30 isalso received by the detector heads 20, and transmission projection datais generated. The transmission data is normally truncated due to thesize of the detector heads 20 or by virtue of the type of collimators 24used. Where a transmission scan is performed, a sorter 200 sorts theemission projection data and transmission projection data on the basisof their relative energies. The data is stored in a projection viewmemory 110, more specifically, in corresponding emission memory 112 andtransmission memory 114.

A data processor 120 takes the emission data from the emission memory112, and corrects the emission data in accordance with attenuationfactors stored in a memory 130. The attenuation factors are determinedfrom a non-uniform attenuation map whose generation is discussed ingreater detail later herein. For each ray along which emission data isreceived, the data processor 120 calculates the projection of acorresponding ray through the transmission attenuation factors stored inthe memory 130. Each ray of the emission data is then weighted orcorrected in accordance with the attenuation factors and reconstructedby a reconstruction processor 140 to generate a three-dimensionalemission image representation that is stored in a volumetric imagememory 300. In a preferred embodiment, the reconstruction performed is afiltered backprojection, maximum likelihood-expectation maximization(ML-EM) algorithm, ordered subset-expectation maximization (OS-EM)algorithm, or other appropriate reconstruction. A video processor 310withdraws and formats selected portions of the data from the imagememory 300 to generate corresponding human-readable displays on a videomonitor 320 or other rendering device. Typical displays includereprojections, selected slices or planes, surface renderings, and thelike.

With reference to FIGS. 2 and continuing reference to FIG. 1, thetechnique is illustrated for generating the non-uniform attenuation map460 which is ultimately used to correct the emission data from the SPECTscan. The first step is to collect a population of a priori transmissionimages (i.e., a “knowledge set”) which are stored in what is nominallytermed an a priori image memory 400. The a priori transmission imagesare not from the patient currently under examination. Rather, they arecross-sections of similar structure. That is to say, they aretransmission images from other subjects of the particular region ofinterest currently being imaged for the patient. In a preferredembodiment, the a priori transmission images are refined and/orpre-processed to remove truncated edges and other reconstructionartifacts. The a priori transmission images are optionally obtained fromCT scans, PET transmission scans, other SPECT transmission scans, andthe like. In a preferred embodiment, the population includes on theorder of 1000 a priori transmission images.

The next step is to generate a cross-correlation matrix 410 from theknowledge set. With the knowledge set having n members being denoted by{X_(i)}, and where the index, i, denotes an order number of the a prioritransmission image, X; the cross-correlation matrix, R, is constructedaccording to the following definition: $\begin{matrix}{R = {\sum\limits_{i}^{n}\quad {X_{i} \cdot {X_{i}^{T}.}}}} & (1)\end{matrix}$

The next step is to calculate the eigenvectors 420 of thecross-correlation matrix 410. In a preferred embodiment, aKarhunen-Loève transform or expansion is employed to derive theeigenvectors 420 of the cross-correlation matrix 410. The Karhunen-Loevetransform is a unitary transform that performs a complete decorrelationbetween transform coefficients.

A set of orthonormal basis vectors 430 is generated from theeigenvectors 420. The set of orthonormal basis vectors 430 isconstructed from a predetermined number of selected eigenvectors chosenfrom the eigenvectors 420 of the cross-correlation matrix 410. Theselected eigenvectors have corresponding eigenvalues that are largerthan the eigenvalues of non-selected eigenvectors. That is to say, thoseeigenvectors 420 having the largest eigenvalues are chosen. In apreferred embodiment, the eigenvectors 420 are ordered according totheir eigenvalues, and a predetermined number are taken off the tophigh-eigenvalue end. In a preferred embodiment, 15% or less of theeigenvectors 420 are chosen. Optionally, the processing of this step isselectively tunable to allow any of a range of predetermined number ofeigenvectors to be selected.

Next, a linear combination of the basis vectors is constructed 440, andcoefficients for the basis vectors are determined 450 such that thelinear combination thereof defines the non-uniform attenuation map 460.

Mathematically, the procedure is to find a set of optimal orthonormalbasis vectors {v_(j), j=1, . . . , N}, for {X_(j)} where each X_(i) hasa dimension N. An approximation using m basis vectors is given by:$\begin{matrix}{{{X_{i} = {{\sum\limits_{j = 1}^{m}\quad {b_{ij} \cdot v_{j}}} + r_{im}}};\quad {i = 1}},2,\ldots \quad,n,} & (2)\end{matrix}$

where r_(im) is the residual error, and b_(j) are the coefficients ofthe basis vectors. In order to find the optimal basis vectors {v_(j)},the residual norms are minimized, that is: $\begin{matrix}{{\sum\limits_{i = 1}^{n}\quad {{}r_{im}{}^{2}}} = {{\sum\limits_{j = {m + 1}}^{n}\quad {{V_{j}^{T}\left( {\sum\limits_{i = 1}^{n}\quad {X_{i}X_{i}^{T}}} \right)}v_{j}}} = {\sum\limits_{j = {m + 1}}^{n}\quad {v_{j}^{T}{Rv}_{j}}}}} & (3)\end{matrix}$

is minimized. Next, the quadratic form from equation (3) is minimizedwith the constraint v_(j) ^(T)v_(j)=1. The extremums of this quadraticform correspond to the eigenvectors of the matrix R. This procedurefinds the optimal basis set in the sense that the average of thedifferences between members of a given set of a priori images, and theirtruncated linear expansion for any basis set, is minimal for thisparticular set. This procedure is the foundation for deriving theKarhunen-Loève transform. Its basis vectors are often referred to asprincipal components. Additionally, one of the properties of theKarhunen-Loève transform is that the eigenvalue λ_(j), normalized by thenumber of images from a knowledge set, represents the average value ofb_(j) ² for the whole knowledge set, that is: $\begin{matrix}{{{\sum\limits_{i = 1}^{n}\quad b_{ij}^{2}} = {{{v_{j}^{T}\left( {\sum\limits_{i = 1}^{n}\quad {X_{i}X_{i}^{T}}} \right)}v_{j}} = {{v_{j}^{T}{Rv}_{j}} = \lambda_{j}}}},} & (4)\end{matrix}$

which implies that: $\begin{matrix}{{{\frac{1}{\lambda_{j}}{\sum\limits_{i = 1}^{n}\quad b_{ij}^{2}}} = 1};\quad {{for}\quad {all}\quad {j.}}} & (5)\end{matrix}$

Equations (4) and (5) are valid only for images from the knowledge set,and the distribution property from equation (4) for the magnitudes ofthe expansion coefficients is expected for each image of similarstructure. The eigenvalues λ_(j) represent variance of the principalcomponents.

In a preferred embodiment, where a transmission scan has been performedand/or truncated transmission projections from the patient currentlybeing imaged are otherwise available from the transmission memory 114,the coefficients for the basis vectors are determined by iterativelycomparing projections of the set of orthonormal basis vectors havingestimated coefficients with truncated transmission projections from thesubject. Using a least-squares fit, the coefficients are select whichbest match the projections of the set of orthonormal basis vectors tothe truncated transmission projections from the patient.

More specifically, where I is a test image which is approximatelyrepresented as a truncated linear expansion of a set basis vectorscorresponding to those eigenvectors having the largest eigenvalues, thefollowing equation is obtained: $\begin{matrix}{I = {{\sum\limits_{j = 1}^{N}\quad {\beta_{j}v_{j}}} \approx {\sum\limits_{j = 1}^{m}\quad {\beta_{j}{v_{j}.}}}}} & (6)\end{matrix}$

The linear relationship is retained in projection space, such that whereP is the linear projection operator, then: $\begin{matrix}{{P(I)} \approx {\sum\limits_{j = 1}^{m}\quad {\beta_{j} \cdot {P\left( v_{j} \right)}}}} & (7)\end{matrix}$

is the expansion in projection space. In practice, P(I) (i.e., thetruncated transmission data) has been acquired and the projections ofthe basis vectors {P(v_(j))} are generated. Because the generatedprojections of the basis vectors are no longer orthogonal, a linearleast squares method is used to find the coefficients β_(j) of thelinear expansion. Because relation (7) is not accurate and residualerrors exist, the solution {β_(j)} is unstable. Note that the solutionfrom relation (7) may not be the same solution from relation (6) due tothe non-orthogonality of basis projections. To stabilize the solution, aconstrained linear inversion method is applied.

Equation (4) indicates that if the text image is similar to those imagesin the knowledge set, β_(j) ²/λ_(j) is approximately a constant for allj. This is seen by interpreting the summation in equation (5) as thestatistical average over the knowledge set. The normalized energy of anexpansion is defined as Σβ_(j) ²/λ_(j), which is rewritten as β^(T)Λβ,where Λ is a diagonal matrix of inverse eigenvalues. Thus, thisnormalized energy is used to regularize the least-squares problem. Thisminimal energy constraint encourages large β_(j) ² for a largeeigenvalue λ_(j), and small β_(j) ² for a small eigenvalue λ_(j).

Looking at equation (4) from a different point of view, the firsteigenvector, corresponding to the largest eigenvalue of thecross-correlation matrix 410 of the knowledge set, is considered as theaverage image over all images in the knowledge set. The average of theexpansion coefficients, excluding the first coefficient, for theknowledge set is zero. The corresponding eigenvalues are the standarddeviations of distribution of expansion coefficients. For a solution tothe inverse problem, the expansion coefficient magnitude is made to benot much larger than the corresponding standard deviation and theregularized solution is biased towards the a priori estimate of theaverage image.

The coefficients of the expansion in relation (6) are obtained bysolving the following minimization problem:

min{∥P(I)−Aβ∥ ²+γ·β^(T)Λβ}  (8),

where columns of the matrix A are P(v_(j)) and γ is the constrainparameter. The constrained linear inversion solution is then given by:

β=(A ^(T) A+γΛ)⁻¹ A ^(T) P(I)  (9),

where a QR decomposition method is used to find the solution to equation(9).

In another preferred embodiment, where no transmission projections ofthe patient currently being imaged are collected or otherwise madeavailable from the transmission memory 114, the coefficients for thebasis vectors are determined by iteratively employing Natterer's dataconsistency conditions to relate emission data from the subject totransmission projections. The transmission projections are generatedfrom projections of the set of orthonormal basis vectors havingestimated coefficients. Using a linear least-squares fit, thecoefficients are selected which generate the transmission projectionsthat best fulfill Natterer's data consistency conditions. Natterer'sdata consistency condition for SPECT is mathematically represented bythe following equation: $\begin{matrix}{{{\int_{0}^{2\pi}{\int_{- \infty}^{\infty}{s^{m}^{\quad k\quad \Phi}^{\frac{1}{2}{\lbrack{{T{({\Phi,s})}} + {\quad {{HT}{({\Phi,s})}}}}\rbrack}}{E\left( {\Phi \quad,s} \right)}\quad {s}\quad {\Phi}}}} = 0};\quad {{{for}\quad 0} \leq m < k};} & (10)\end{matrix}$

where E represents the emission data, T represents transmissionline-integrals, and H is the Hilbert transform with respect to s. Inequation (10), T(φ,s) is not available due to the lack of measuredtransmission data, and it is therefore modeled as follows:$\begin{matrix}{{{T\left( {\Phi,s} \right)} = {{P\left( {\sum\limits_{j = 1}^{m}\quad {\beta_{j}{v_{j}\left( {x,y} \right)}}} \right)} = {{\sum\limits_{j = 1}^{m}\quad {\beta_{j}{P\left( {v_{j}\left( {x,y} \right)} \right)}}} = {\sum\limits_{j = 1}^{m}\quad {\beta_{j}{T_{j}\left( {\Phi,s} \right)}}}}}};} & (11)\end{matrix}$

where v_(j)(x,y) represent the set of orthonormal basis vectors 430, mis the predetermined number of eigenvectors selected to generate the setof basis vectors, P is the projection operator, and β_(j) are theexpansion coefficients to be estimated and/or determined.

In a preferred embodiment, separate dedicated data processors and/orcircuits, application specific and/or otherwise, are employed to carriedout the various steps for generating the non-uniform attenuation map460. As well, the steps are alternately implemented by hardware,software, and/or combinations of hardware and software configurations.Optionally, one or more or all the steps are combined for processing byone integrated data processor or computer.

The invention has been described with reference to the preferredembodiments. Obviously, modifications and alterations will occur toothers upon reading and understanding the preceding detaileddescription. It is intended that the invention be construed as includingall such modifications and alterations insofar as they come within thescope of the appended claims or the equivalents thereof.

Having thus described the preferred embodiments, the invention is nowclaimed to be:
 1. A method of reconstructing a diagnostic imagerepresentation from emission data collected from a patient, the methodcomprising: (a) collecting a set of transmission image representationsincluding transmission image representations from a plurality ofdifferent subjects, each image representation being of like anatomy,said set of transmission image representations not including one of thepatients; (b) generating a cross-correlation matrix from the set oftransmission image representations; (c) calculating eigenvectors of thecross-correlation matrix; (d) generating a set of orthonormal basisvectors from the eigenvectors; (e) constructing a linear combination ofthe basis vectors; (f) estimating transmission projection data bygenerating projection data from the set of orthonormal basis vectorshaving estimated coefficients; (g) generating an attenuation map fromthe estimated transmission projection data; (h) formulating dataconsistency conditions defining a relationship between measured emissiondata collected from the patient and the estimated transmissionprojection data; (i) determining coefficients for the basis vectorswhich generate transmission projections that best fulfill the dataconsistency conditions using a linear least-squares fit; and (j)reconstructing an emission image representation from the emission dataand the determined coefficients.
 2. The method according to claim 1,wherein the data consistency conditions are Natterer's data consistencyconditions.
 3. An image processor for reconstructing images of adistribution of radioactive material in a patient being examined with agamma camera comprising: an emission memory which stores emission datacollected by the gamma camera; an attenuation factor memory which storesattenuation factors calculated from a non-uniform attenuation map; adata processor which takes the emission data and corrects it forattenuation in accordance with the attenuation factors stored in theattenuation factor memory; a reconstruction processor that takescorrected emission data from the data processor and therefromreconstructs an image representation of the distribution of radioactivematerial in the patient; an a priori image memory that stores a prioritransmission data from a plurality of a priori transmission scans of aregion of interest that is the same as that being reconstructed, saidtransmission scans originating from subjects other than the patient; across-correlation data processor that constructs a cross-correlationmatrix from the a priori transmission scans; an eigenvector dataprocessor that calculates eigenvectors of the cross-correlation matrix;a basis data processor that constructs a set of orthonormal basisvectors from the eigenvectors of the cross-correlation matrix; and, aniterative data processor that computes coefficients for the basisvectors such that a linear combination thereof defines the non-uniformattenuation map.
 4. The image processor according to claim 3, whereinthe eigenvector data processor employs a Karhunen-Loève transform tocalculate the eigenvector of the cross-correlation matrix.
 5. The imageprocessor according to claim 3, wherein the basis data processorconstructs the set of orthonormal basis vectors by selecting apredetermined number of the eigenvectors, wherein the eigenvectorsselected have corresponding eigenvalues greater than any eigenvalue ofthose eigenvectors not selected.
 6. The image processor according toclaim 5, wherein the basis data processor is tunable by altering thepredetermined number of the eigenvectors selected.
 7. The imageprocessor according to claim 5, wherein the predetermined number of saidselected eigenvectors selected by the basis data processor is less thanor equal to approximately 15% of the eigenvectors of thecross-correlation matrix calculated by the eigenvalue data processor. 8.The image processor according to claim 3, wherein the iterative dataprocessor: estimates transmission projection data by generatingprojection data from the set of orthonormal basis vectors havingestimated coefficients; formulates data consistency conditions, the dataconsistency conditions defining a relationship between measured emissiondata from the subject and the estimated transmission projection data;and identifies coefficients for the basis vectors which generatetransmission projection data that best fulfill the data consistencyconditions.
 9. The image processor according to claim 8, wherein thedata consistency conditions are Natterer's data consistency conditions.10. The image processor according to claim 3, wherein no transmissiondata from the gamma camera is used in reconstructing images of thedistribution of radioactive material in the patient.
 11. An imageprocessor for reconstructing images of a distribution of radioactivematerial in a first patient being examined with a gamma camera,comprising: an a priori image memory that stores a priori transmissiondata from a plurality of a priori transmission scans of a region ofinterest that corresponds to a region to be reconstructed, said a prioritransmission data originating from subjects other than the firstpatient; a cross-correlation data processor that constructs across-correlation matrix from the a priori transmission data; a vectorprocessor that constructs a set of orthonormal basis vectors from thecross-correlation matrix; a transmission memory which stores truncatedtransmission projections of the first patient collected by the gammacamera; an iterative data processor which (i) iteratively comparesprojections of linear combination of basis vectors with estimatedcoefficients to the truncated transmission projections, and (ii) selectscoefficients which best match the projections of the linear combinationof basis vectors to the truncated transmission projections; anattenuation factor memory which stores the selected coefficients; anemission memory which stores emission data collected by the gammacamera; a correction processor which corrects emission data forattenuation in accordance with the selected coefficients stored in theattenuation factor memory; a reconstruction processor that reconstructsthe corrected emission data into an image representation of thedistribution of radioactive material in the first patient.
 12. A methodof reconstructing a diagnostic image representation from measuredemission radiation from a subject to be imaged, comprising: collectingprojection data including measured emission projection data from thesubject; collecting a knowledge set comprising a plurality oftransmission image representations, the plurality of transmission imagerepresentations generated from a corresponding section of similarstructure of a plurality of subjects other than the subject to beimaged; using the knowledge set to generate an attenuation map whichprovides an estimate of radiation attenuation properties of the subjectto be imaged; and reconstructing an emission image representation fromthe emission projection data and the attenuation map.
 13. A methodaccording to claim 12, wherein the attenuation map is generated by: (a)generating a cross-correlation matrix from the knowledge set oftransmission images; (b) calculating eigenvectors of thecross-correlation matrix; (c) generating a set of orthonormal basisvectors from the eigenvectors; (d) constructing a linear combination ofthe basis vectors; and, (e) determining coefficients for the basisvectors such that the linear combination thereof defines the non-uniformattenuation map.
 14. The method according to claim 13, wherein aKarhunen-Loève transform is employed to calculate the eigenvectors ofthe cross-correlation matrix.
 15. The method according to claim 13,wherein the set of orthonormal basis vectors is constructed from apredetermined number of selected eigenvectors chosen from theeigenvectors of the cross-correlation matrix, said selected eigenvectorshaving corresponding eigenvalues larger than eigenvalues of non-selectedeigenvectors of the cross-correlation matrix.
 16. The method accordingto claim 15, wherein the predetermined number of said selectedeigenvectors is less than or equal to approximately 15% of thecalculated eigenvectors of the cross-correlation matrix.
 17. The methodaccording to claim 13, wherein the step of determining coefficients forthe basis vectors comprises: iteratively comparing projections of theset of orthonormal basis vectors having estimated coefficients withtruncated transmission projections from the subject; and, using aleast-squares fit to select coefficients which best match theprojections of the set of orthonormal basis vectors to the truncatedtransmission projections from the subject.
 18. The method according toclaim 13, wherein no transmission scan of the subject is performed. 19.The method according to claim 12, wherein the attenuation map isgenerated using an eigenvector analysis.
 20. The method according toclaim 12, wherein the knowledge set is correlated with the measuredemission projection data.
 21. The method according to claim 12, whereinthe measured projection data further includes measured transmissionprojection data, and further wherein the knowledge set is correlatedwith the measured transmission projection data.
 22. The method accordingto claim 21, wherein the measured transmission projection data istruncated.
 23. The method according to claim 12, wherein and at leastone transmission image representation is of an imaging modalitydifferent from the emission image representation.
 24. A method ofconstructing a non-uniform attenuation map for use in reconstructing adiagnostic image representation from measured emission radiationprojection data of a first imaged subject, comprising: collecting aknowledge set comprising a plurality of transmission imagerepresentations, the plurality of transmission image representationsgenerated from a corresponding section of similar structure of one ormore subjects other than the first imaged subject; and generating anattenuation map which provides an estimate of radiation attenuationproperties of the first imaged subject using the knowledge set.